In a different approach to the construction of the nonlinear weights,
Borges et al. [1]}, introduced the fifth-order
WENO-Z scheme. In their study, the authors measured the smoothness
of the large stencil which comprises all sub-stencils and incorporated
this in devising the smoothness indicators and nonlinear weights.
The resulting WENO-Z scheme is less dissipative than WENO-JS and WENO-M.
The convergence order of the WENO-Z scheme is four at the first-order
critical points and degrade to two when higher order critical points
are encountered. Further, a closed-form formula was derived in [2]}
for the WENO-Z scheme to the all odd orders, higher than fifth-order
accuracy.
